The Indecomposable Solutions of Linear Congruences
| Autor: | Pommerening, Klaus |
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| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | This article considers the minimal non-zero (= indecomposable) solutions of the linear congruence $1\cdot x_1 + \cdots + (m-1)\cdot x_{m-1} \equiv 0 \pmod m$ for unknown non-negative integers $x_1, \ldots, x_n$, and characterizes the solutions that attain the Eggleton-Erd\H{o}s bound. Furthermore it discusses the asymptotic behaviour of the number of indecomposable solutions. The results have direct interpretations in terms of zero-sum sequences and invariant theory. Comment: 23 pages, 1 figure. Updated version: Former Theorem 2 attributed to Eggleton and Erd\H{o}s, proof deleted. Some elementary considerations deleted, some minor modifications. Added references |
| Databáze: | arXiv |
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